Among white cancer patients significant increases in survival over the 10 year span from 1960-63 to 1970-73 were observed for 7 of the 10 most frequently occurring cancers (Lung, Stomach and Pancreas were the exceptions). Among black patients significant increases were noted for cancers of the uterine corpus, uterine cervix, urinary Bladder and prostate. The most remarkable improvements in survival were observed for Acute Lymphocytic Leukemia in Children less than 15. A newly developed age-dependent mathematical model for cancer screening has lead to a more complete understanding of length bias than had previously been possible. Women with lobular carcinoma in situ are at an increased risk of developing subsequent contralateral carcinoma. No elevated risk was observed for intraductal carcinoma. Cervical cancer patients treated by radiotherapy are at an increased risk of developing leukemia and cancers of the lung, bladder, kidney and genital organs. Adjustment of black-white differences in incidence of breast and cervical cancer for socioeconomic levels explained substantial portions of the observed differences for each site. A statistical method utilizing the interval of time between successive diagnoses of cancers has application in monitoring time trends of cancer incidence and for assessment of disease clustering.